To meet the requirement of six usable IP addresses, the subnet mask 255.255.255.240 (also represented as /28) is the best fit. A /28 subnet provides 16 total IP addresses, out of which 14 are usable (the first address is the network address, and the last address is the broadcast address). This meets and exceeds the requirement for six usable IP addresses, ensuring there are enough addresses for future expansion if needed. The other options provide either too few or too many addresses for this specific requirement.
Reference: CompTIA Network+ Certification Exam Objectives - IP Addressing section.